To test your manifest file, you'll have to push a build of your game to itch.io - ideally, using https://itch.io/docs/butler/ - so that you can push any changes quickly instead of having to reupload the whole thing.

Then, simply install and launch your game from the itch app. You can open the game's "event log" (which contains information about problems with the manifest, among other things) by right-clicking the game's tab, opening "View log":